(The) ergodicity of skew products

Abstract

We define an automorphism T by the formula T(u,z)=(T$_2$u,s(u)z) where T$_2$ is an integral automorphism over the automorphism T$_1$(T$_1$x=x+$\beta$ (modl)) with the function F and s(u) depends only on x variable, $u=(x,y),\; z \in Z_{n+1}$. And we show that T has nonsimple finite multiplicity continuous spectrum.